An industrial liquid flows through a section of a pipe with an area of cross-section 2 m2 at a velocity of 10 m/s. If at a certain section the area of cross-section decreases to 1 m2, then the velocity of the liquid will be
Correct answer: D. 20 m/s
- A. 5 m/s
- B. 10 m/s
- C. 15 m/s
- D. 20 m/s
Explanation
According to the principle of continuity for fluid flow, the product of the cross-sectional area and velocity of a fluid must remain constant within an enclosed system. This can be expressed as A1 * V1 = A2 * V2. Initially, the area A1 is 2 m² and the velocity V1 is 10 m/s. When the area is reduced to 1 m² (A2), the new velocity (V2) must be calculated. Substituting the known values: 2 m² * 10 m/s = 1 m² * V2, which simplifies to V2 = 20 m/s. Therefore, the correct answer is 20 m/s. The other options are incorrect because they do not satisfy this relationship.
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About Equation of Continuity
The equation of continuity expresses conservation of mass in fluid flow. For steady incompressible flow, Av remains constant, so fluid speed increases when the cross-sectional area decreases; for compressible flow, ρAv is constant. This relation describes flow rate and area-speed changes without including pressure effects from Bernoulli’s equation.
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